Abstract

We report on the experimental visualization of the cladding Bloch-modes of a hollow-core photonic crystal fiber. Both spectral and spatial field information is extracted using the approach, which is based on measurement of the near-field and Fresnel-zone that results after propagation over a short length of fiber. A detailed study of the modes near the edges of the band gap shows that it is formed by the influence of three types of resonator: the glass interstitial apex, the silica strut which joins the neighboring apexes, and the air hole. The cladding electromagnetic field which survives the propagation is found to be spatially coherent and to contain contributions from just a few types of cladding mode.

© 2007 Optical Society of America

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  1. B. J. Mangan, L. Farr, A. Langford,  et al., "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," presented at the OFC 2004, 2004.
  2. F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).
  3. F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
    [CrossRef] [PubMed]
  4. S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
    [CrossRef] [PubMed]
  5. F. Benabid, P. S. Light, F. Couny,  et al., "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694 (2005).
    [CrossRef] [PubMed]
  6. F. Couny, P.S. Light, F. Benabid,  et al., "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006).
    [CrossRef]
  7. T. A. Birks, P. J. Roberts, P. S. J. Russell,  et al., "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
    [CrossRef]
  8. G. Humbert, J. Knight, G. Bouwmans,  et al., "Hollow core photonic crystal fibers for beam delivery," Opt. Express 12, 1477-1484 (2004).
    [CrossRef] [PubMed]
  9. J. West, C. Smith, N. Borrelli,  et al., "Surface modes in air-core photonic band-gap fibers," Opt. Express 12, 1485-1496 (2004).
    [CrossRef] [PubMed]
  10. K. Saitoh, N. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12, 394-400 (2004).
    [CrossRef] [PubMed]
  11. T. A. Birks, D. M. Bird, T. Hedley,  et al., "Scaling laws and vector effects in bandgap-guiding fibres," Opt. Express 12, 69-74 (2003).
    [CrossRef]
  12. F. Benabid and P. St. J. Russell, "Hollow-core PCF; progress and prospects," Proc. SPIE 5733, 176-190 (2005).
    [CrossRef]
  13. G. Antonopoulos, F. Benabid, T. A. Birks,  et al., "Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling," Opt. Express 14, 3000-3006 (2006).
    [CrossRef] [PubMed]
  14. P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
    [CrossRef]
  15. P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
    [CrossRef]
  16. P. Yeh, Optical waves in layered media (John Wiley and Sons, New York, 1988).
  17. M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
    [CrossRef]
  18. N. Litchinitser, S. Dunn, B. Usner,  et al., "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
    [CrossRef] [PubMed]
  19. N. M. Litchinister, A. K. Abeeluck, C. Headley,  et al., "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1320-1323 (2002).
  20. T. A. Birks, G. J. Pearce, and D. M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483-9490 (2006).
    [CrossRef] [PubMed]
  21. N. W. Aschcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, PA 19105, 1976).
  22. T. P. White, R. C. McPhedran, C. M. De Sterke,  et al., "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
    [CrossRef]
  23. J. Lægsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
    [CrossRef]
  24. P. Steinvurzel, C. M. De Sterke, M. J. Steel,  et al., "Single scatterer Fano resonances in solid core photonic band gap fibers," Opt. Express 14, 8797-8811 (2006).
    [CrossRef] [PubMed]
  25. Here the triangular lattice labeling refers to the placement of the air holes. Though the cladding structure of the fiber could be seen as a set of silica rods aligned in a honeycomb lattice, we keep the triangular labeling for historical reasons.
  26. J. B. Jensen, L. H. Pedersen, P. E. Hoiby,  et al., "Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions," Opt. Lett. 29, 1974-1976 (2004).
    [CrossRef] [PubMed]
  27. C. M. Smith, N. Venkataraman, M. T. Gallagher,  et al., "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  28. P. J. Roberts, F. Couny, H. Sabert,  et al., "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
    [CrossRef] [PubMed]
  29. T. D. Hedley, D. M. Bird, F. Benabid,  et al., "Modelling of a novel hollow-core photonic crystal fibre," presented at the Quantum Electronics and Laser Science, 2003. QELS. Postconference Digest, pp. 2, (2003).
  30. J. M. Pottage, D. M. Bird, T. D. Hedley,  et al., "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003).
    [CrossRef] [PubMed]
  31. N. A. Mortensen and M. D. Nielsen, "Modeling of realistic cladding structures for air-core photonic bandgap fibers," Opt. Lett. 29, 349-351 (2004).
    [CrossRef] [PubMed]
  32. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  33. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  34. J. D. Shephard, P. J. Roberts, J. D. C. Jones,  et al., "Measuring beam quality of Hollow Core Photonic Crystal Fibers," J. Lightwave Technol. 24, 3761-3769 (2006).
    [CrossRef]

2006 (5)

2005 (5)

P. J. Roberts, F. Couny, H. Sabert,  et al., "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

F. Benabid, P. S. Light, F. Couny,  et al., "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694 (2005).
[CrossRef] [PubMed]

F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).

F. Benabid and P. St. J. Russell, "Hollow-core PCF; progress and prospects," Proc. SPIE 5733, 176-190 (2005).
[CrossRef]

S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

2004 (6)

2003 (4)

2002 (3)

T. P. White, R. C. McPhedran, C. M. De Sterke,  et al., "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

N. M. Litchinister, A. K. Abeeluck, C. Headley,  et al., "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1320-1323 (2002).

F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

2001 (1)

1997 (1)

1995 (1)

T. A. Birks, P. J. Roberts, P. S. J. Russell,  et al., "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

1986 (1)

M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

1978 (1)

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
[CrossRef]

1976 (1)

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Abeeluck, A. K.

N. M. Litchinister, A. K. Abeeluck, C. Headley,  et al., "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1320-1323 (2002).

Antonopoulos, G.

G. Antonopoulos, F. Benabid, T. A. Birks,  et al., "Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling," Opt. Express 14, 3000-3006 (2006).
[CrossRef] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

Benabid, F.

G. Antonopoulos, F. Benabid, T. A. Birks,  et al., "Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling," Opt. Express 14, 3000-3006 (2006).
[CrossRef] [PubMed]

F. Couny, P.S. Light, F. Benabid,  et al., "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006).
[CrossRef]

F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).

F. Benabid and P. St. J. Russell, "Hollow-core PCF; progress and prospects," Proc. SPIE 5733, 176-190 (2005).
[CrossRef]

F. Benabid, P. S. Light, F. Couny,  et al., "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694 (2005).
[CrossRef] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

Bird, D. M.

Birks, T. A.

Borrelli, N.

Bouwmans, G.

Couny, F.

F. Couny, P.S. Light, F. Benabid,  et al., "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006).
[CrossRef]

F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).

P. J. Roberts, F. Couny, H. Sabert,  et al., "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

F. Benabid, P. S. Light, F. Couny,  et al., "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694 (2005).
[CrossRef] [PubMed]

De Sterke, C. M.

Duguay, M. A.

M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Dunn, S.

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher,  et al., "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Ghosh, S.

S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Headley, C.

N. M. Litchinister, A. K. Abeeluck, C. Headley,  et al., "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1320-1323 (2002).

Hedley, T.

Hedley, T. D.

Hoiby, P. E.

Humbert, G.

Jensen, J. B.

Joannopoulos, J. D.

Johnson, S. G.

Jones, J. D. C.

Knight, J.

Knight, J. C.

F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).

F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

Koch, T. L.

M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Koshiba, M.

Kukubun, Y.

M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Lægsgaard, J.

J. Lægsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

Light, P. S.

Light, P.S.

F. Couny, P.S. Light, F. Benabid,  et al., "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006).
[CrossRef]

Litchinister, N. M.

N. M. Litchinister, A. K. Abeeluck, C. Headley,  et al., "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1320-1323 (2002).

Litchinitser, N.

Marom, E.

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
[CrossRef]

McPhedran, R. C.

Mortensen, N.

Mortensen, N. A.

Nielsen, M. D.

Ouzounov, D. G.

S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Pearce, G. J.

Pedersen, L. H.

Pottage, J. M.

Roberts, P. J.

Russell, P. S. J.

T. A. Birks, P. J. Roberts, P. S. J. Russell,  et al., "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Russell, P. St. J.

F. Benabid and P. St. J. Russell, "Hollow-core PCF; progress and prospects," Proc. SPIE 5733, 176-190 (2005).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

Sabert, H.

Saitoh, K.

Sharping, J.

S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Shephard, J. D.

Smith, C.

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher,  et al., "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Steel, M. J.

Steinvurzel, P.

Usner, B.

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher,  et al., "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

West, J.

White, T. P.

Yariv, A.

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
[CrossRef]

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
[CrossRef]

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kukubun, T. L. Koch,  et al., "Antiresonant reflecting optical waveguides in Sio2-Si multilayer strucutures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Electron. Lett. (1)

T. A. Birks, P. J. Roberts, P. S. J. Russell,  et al., "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A: Pure Appl. Opt. (1)

J. Lægsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

J. Opt. Soc. Am (1)

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am 68, 1196-1201 (1978).
[CrossRef]

Nature (2)

C. M. Smith, N. Venkataraman, M. T. Gallagher,  et al., "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

F. Benabid, F. Couny, J. C. Knight,  et al., "Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres," Nature 434, 488-491 (2005).

Opt. Commun. (2)

F. Couny, P.S. Light, F. Benabid,  et al., "Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber," Opt. Commun. 263, 28-31 (2006).
[CrossRef]

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Opt. Express (12)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

P. J. Roberts, F. Couny, H. Sabert,  et al., "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

F. Benabid, P. S. Light, F. Couny,  et al., "Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF," Opt. Express 13, 5694 (2005).
[CrossRef] [PubMed]

G. Antonopoulos, F. Benabid, T. A. Birks,  et al., "Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling," Opt. Express 14, 3000-3006 (2006).
[CrossRef] [PubMed]

P. Steinvurzel, C. M. De Sterke, M. J. Steel,  et al., "Single scatterer Fano resonances in solid core photonic band gap fibers," Opt. Express 14, 8797-8811 (2006).
[CrossRef] [PubMed]

T. A. Birks, G. J. Pearce, and D. M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483-9490 (2006).
[CrossRef] [PubMed]

N. Litchinitser, S. Dunn, B. Usner,  et al., "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley,  et al., "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003).
[CrossRef] [PubMed]

T. A. Birks, D. M. Bird, T. Hedley,  et al., "Scaling laws and vector effects in bandgap-guiding fibres," Opt. Express 12, 69-74 (2003).
[CrossRef]

K. Saitoh, N. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12, 394-400 (2004).
[CrossRef] [PubMed]

G. Humbert, J. Knight, G. Bouwmans,  et al., "Hollow core photonic crystal fibers for beam delivery," Opt. Express 12, 1477-1484 (2004).
[CrossRef] [PubMed]

J. West, C. Smith, N. Borrelli,  et al., "Surface modes in air-core photonic band-gap fibers," Opt. Express 12, 1485-1496 (2004).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

S. Ghosh, J. Sharping, D. G. Ouzounov,  et al., "Resonant optical interactions with molecules confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Proc. SPIE (1)

F. Benabid and P. St. J. Russell, "Hollow-core PCF; progress and prospects," Proc. SPIE 5733, 176-190 (2005).
[CrossRef]

Science (1)

F. Benabid, J. C. Knight, G. Antonopoulos,  et al., "Stimulated Raman Scattering in Hydrogen-filled hollow-core Photonic Crystal Fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

Other (5)

B. J. Mangan, L. Farr, A. Langford,  et al., "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," presented at the OFC 2004, 2004.

N. W. Aschcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, PA 19105, 1976).

P. Yeh, Optical waves in layered media (John Wiley and Sons, New York, 1988).

T. D. Hedley, D. M. Bird, F. Benabid,  et al., "Modelling of a novel hollow-core photonic crystal fibre," presented at the Quantum Electronics and Laser Science, 2003. QELS. Postconference Digest, pp. 2, (2003).

Here the triangular lattice labeling refers to the placement of the air holes. Though the cladding structure of the fiber could be seen as a set of silica rods aligned in a honeycomb lattice, we keep the triangular labeling for historical reasons.

Supplementary Material (3)

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Figures (7)

Fig. 1.
Fig. 1.

(a). Scanning electron micrograph of a HC-PCF which guides within its core at 1064nm. (b). Details of the cladding structure used for the numerical modeling.

Fig. 2.
Fig. 2.

(a). Propagation diagram for a triangular HC-PCF cladding lattice. Black represents zero DOS and white maximum DOS. The upper x-axis shows the corresponding wavelengths for a HC-PCF guiding at 800 nm (Λ=2.15μm). The trajectory of the cladding modes on the edges of the PBG are represented in red for the interstitial apexes mode and by the letter (b), in blue for the silica strut mode (c) and in green for the air hole mode (d). The lower figures show the near field of the “apex” mode (b), the “strut” mode (c) and the “airy” mode (d). The first two modes are shown at an effective index of 0.995 (represented by the dash-dotted white line), whereas the airy mode is shown at kΛ=15.5 and neff =0.973. The solid lines show the Γ-point mode trajectories and the dotted lines the J-point mode trajectories. (e) DOS diagram extended to a normalized frequency kΛ=45. (f) Brillouin zone symmetry point nomenclature.

Fig. 3.
Fig. 3.

(2.24Mo each). Evolution of calculated Fresnel zone patterns of the apex mode (a) and the strut mode (b). The propagation starts at z=0 and ends at z=2Λ. Two adjacent frames in the animation correspond to a spatial separation of 0.1Λ. Representative frames for both modes are shown in Fig. 5. [Media 1] [Media 2]

Fig. 4.
Fig. 4.

(2.15Mo) Evolution of measured Fresnel-zone patterns of a transmitted cladding mode for different distances from the output end of a 3 mm long HC-PCF. [Media 3]

Fig. 5.
Fig. 5.

(A). Calculated near-field profile for the apex mode (A1), strut mode (A2) and airy mode (A3). (B) Corresponding Fresnel zone mode patterns. The position of the diffraction pattern is 1.8Λ, 1.5Λ and 2.0Λ away from the fiber for the three modes respectively. (C) Observed Fresnel zone mode patterns for a wavelength of 950nm, 750nm and 700nm in a HC-PCF guiding around 800nm. The pattern positions, relative to the end of the fiber, are in the range of 4-5μm.

Fig. 6.
Fig. 6.

Optical spectrum of HC-PCF guiding around 1550nm collected through the SNOM tip when aligned with the centre of fiber core (black line) or close to a cladding air-hole, two rings away from the fiber core (grey line). (B) SNOM near-field profiles of the HC-PCF guiding around 1550nm in the vicinity of the core as a function of the filtered wavelength. White noise in the 1400nm picture comes from an increase in sensitivity due to low level of light being guided.

Fig. 7.
Fig. 7.

(A). SNOM images of the (1) “apex” mode (2) “strut” mode and (3) “airy” mode of the fiber cladding. (B) Optical spectrum of the HC-PCF guiding around 800nm taken with the SNOM tip aligned with the core (black line) and the cladding (grey line), (C) Optical spectrum of the HC-PCF guiding around 1064nm taken with the SNOM tip aligned (top) with the core, (bottom) with an interstitial apex (black solid line) and with an air hole of the cladding (grey doted line). The peaks around 1064nm are due to the residual super-continuum pump.

Equations (4)

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v g⊥ ( n ) / c = k k n k β ,
ρ k β = 1 ( 2 π ) 3 n 1 st BZ d 2 k δ ( k k n ( k , β ) )
= 1 ( 2 π ) 3 n C n d l 1 k k n k β c ( 2 π ) 3 n C n d l 1 v g ( n ) ,
L << 2 π Δ β = λ Δ n ,

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